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In $25-30,$ perform the indicated operations and write the result in simplest form. In each case, list any values of the variables for which the fractions are not defined.$$\frac{x^{2}-3 x+2}{4 x} \cdot \frac{12 x^{2}}{x^{2}-2 x} \div \frac{x-1}{x}$$

$3 x ; x \neq 0,2$

Algebra

Chapter 2

THE RATIONAL NUMBERS

Section 3

Multiplying and Dividing Rational Expressions

Fractions and Mixed Numbers

Decimals

Equations and Inequalities

Missouri State University

Campbell University

Oregon State University

Harvey Mudd College

Lectures

01:32

In mathematics, the absolu…

01:11

01:35

In $25-30,$ perform the in…

01:49

00:53

In $3-20$ , perform the in…

03:04

05:52

04:55

00:35

Simplify each rational exp…

01:59

In $3-12,$ multiply and ex…

00:49

06:28

So for this question, were given a series of fractions were asked to perform a series of operations on them. I'm just going to look at the 1st 2 so I'm going to factor out the numerator here. To be X minus two or times X minus. Waas over for X is being multiplied by a 12 x square and factory out of X here. That will give us X minus two. So from here, we can say that our X value cannot be equal to zero or two, as that would make these denominators equal to zero. So now we can cancel her before here before here, making this three in this actual cancel with one of these X is making this three X. Now, we can say that this X will cancel with this ex just getting rid of the ex entirely. This X minus to cancel this X minus two. And now we're left with three times X minus one over one. So this will give us an answer of three times X minus one over one. Now it's asking us to the by this answer by X minus one over X, which is the same as multiplying by. There was cyclical of X minus one over X. So you could say that this is equal to three X minus one over one times X over X minus one. So here, in this fraction, ex cannot be zero, and we've already put a limit. Their butt X can also not be equal to one as that, with this denominator equal to zero. So we have to write. X cannot be even one as well. So now we can say that this X minus one cancels with this X minus one. And so we're just left with three acts over one, which is just three X s O. That is our answer.

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